If abc = 1, then 11 + a + b^ - 1 + 11 + b + c^ - 1 + 11 + c + a^ - 1 = ?

Answer: Option B

Given expression,
$$\frac{1}{1+a+b^{-1}}+$$   $$\frac{1}{1+b+c^{-1}}+$$   $$\frac{1}{1+c+a^{-1}}$$
  $$=\frac{1}{1+a+b^{-1}}+$$   $$\frac{b^{-1}}{b^{-1}+1+b^{-1}{c}^{-1}}+$$    $$\frac{1}{a+ac+1}$$
  $$=\frac{1}{1+a+b^{-1}}+$$   $$\frac{b^{-1}}{1+b^{-1}+a}+$$   $$\frac{a}{a+b^{-1}+1}$$
$$\begin{array}{rl}& =\frac{1+a+b^{-1}}{1+a+b^{-1}}\\ & =1\end{array}$$
$$\left[\because abc=1\Rightarrow {\left(bc\right)}^{-1}=a\Rightarrow b^{-1}{c}^{-1}=a,\text{and }ac=b^{-1}\right]$$